Numerical modelling of the growth and remodelling phenomena in biological tissues

Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A new generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a finite-strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.Els teixits biològics vius són estructures complexes que tenen la capacitat d'evolucionar en resposta a càrregues externes i estímuls ambientals. El modelat adequat del comportament del teixit biològic tou és un tema clau per poder reproduir amb èxit problemes biomecànics mitjançant anàlisi computacional. Aquest estudi presenta una formulació constitutiva general capaç de representar el comportament d'aquests teixits mitjançant la simulació amb elements finits. Es basa en models fenomenològics que, usats en combinació amb la teoria de mescles generalitzada, permeten reproduir numèricament un ampli ventall de comportaments materials. Primer, el comportament passiu dels teixits es caracteritza amb models hiperelàstics i de dany en grans deformacions. Es proposa un model generalitzat de dany que proporciona una formulació versàtil i flexible per poder reproduir una extensa gamma de conductes de teixits. Pot ser particularitzat amb qualsevol model hiperelàstic i requereix identificar tan sols dos paràmetres materials. Llavors, es descriu l'ús d'aquests models constitutius en conjunt amb la teoria generalitzada de mescles, desenvolupada en el marc de grans deformacions, i es presenten eines que permeten incorporar les propietats anisòtropes dels teixits. El comportament actiu dels teixits es caracteritza mitjançant models constitutius capaços de reproduir els fenòmens de creixement i remodelació. Aquests es construeixen sobre les formulacions d'hiperelasticitat i dany descrites anteriorment i, per tant, suposen l'extensió activa del comportament passiu del teixit. Es fa servir un model de creixement que té en compte la disponibilitat biològica de l'organisme, que després s'amplia per incloure dany direccional en el model. També es presenta i analitza un nou model constitutiu per al remodelat per renovació tendint a l’homeòstasi (homeostatic-driven turnover remodelling). Aquest model captura la recuperació de rigidesa que s'observa en teixits que es guareixen. Aquí, el remodelat s'entén com la recuperació o inversió del dany en el teixit i és motivat tant per estímuls mecànics com bioquímics. Finalment, s'aborda el tema de la identificació correcta dels paràmetres materials per al modelat computacional. Es desenvolupa un mètode invers que fa ús de tècniques d'optimització per facilitar la identificació d'aquests paràmetre

A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation

A new generalized damage model for quasi‐incompressible hyperelasticity in a total Lagrangian finite‐strain framework is presented. A Kachanov‐like reduction factor (1 − D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric–isochoric split of the Helmholtz free energy. However, in the present work, it has been implemented in an in‐house finite element code for neo‐Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three‐dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature

Optimization method for the determination of material parameters in damaged composite structures

An optimization method to identify the material parameters of composite structures using an inverse method is proposed. This methodology compares experimental results with their numerical reproduction using the finite element method in order to obtain an estimation of the error between the results. This error estimation is then used by an evolutionary optimizer to determine, in an iterative process, the value of the material parameters which result in the best numerical fit. The novelty of the method is in the coupling between the simple genetic algorithm and the mixing theory used to numerically reproduce the composite behavior. The methodology proposed has been validated through a simple example which illustrates the exploitability of the method in relation to the modeling of damaged composite structures.Peer ReviewedPostprint (author’s final draft

The role of computational models in mechanobiology of growing bone

Endochondral ossification, the process by which long bones grow in length, is regulated by mechanical forces. Computational models, specifically finite element models, have been used for decades to understand the role of mechanical loading on endochondral ossification. This perspective outlines the stages of model development in which models are used to: 1) explore phenomena, 2) explain pathologies, 3) predict clinical outcomes, and 4) design therapies. As the models progress through the stages, they increase in specificity and biofidelity. We give specific examples of models of endochondral ossification and expect models of other mechanobiological systems to follow similar development stages.Peer ReviewedPostprint (published version

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

All rights reserved. Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data. Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data

I’m stuck! How to efficiently debug computational solid mechanics models so you can enjoy the beauty of simulations

A substantial fraction of the time that computational modellers dedicate to developing their models is actually spent trouble-shooting and debugging their code. However, how this process unfolds is seldom spoken about, maybe because it is hard to articulate as it relies mostly on the mental catalogues we have built with the experience of past failures. To help newcomers to the field of material modelling, here we attempt to fill this gap and provide a perspective on how to identify and fix mistakes in computational solid mechanics models. To this aim, we describe the components that make up such a model and then identify possible sources of errors. In practice, finding mistakes is often better done by considering the symptoms of what is going wrong. As a consequence, we provide strategies to narrow down where in the model the problem may be, based on observation and a catalogue of frequent causes of observed errors. In a final section, we also discuss how one-time bug-free models can be kept bug-free in view of the fact that computational models are typically under continual development. We hope that this collection of approaches and suggestions serves as a “road map” to find and fix mistakes in computational models, and more importantly, keep the problems solved so that modellers can enjoy the beauty of material modelling and simulation.EC and JPP wish to thank their former supervisor Paul Steinmann for the inspiration to write this paper, which can be traced back to the talk we prepared for the ECCM-ECFD conference held in Glasgow in 2018. EC’s work was partially supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 841047. WB’s work was partially supported by the National Science Foundation under award OAC-1835673; by award DMS-1821210; by award EAR-1925595; and by the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under Award EAR-1550901 and The University of California – Davis .Peer ReviewedPostprint (published version

Optimization method for the determination of material parameters in damaged composite structures

An optimization method to identify the material parameters of composite structures using an inverse method is proposed. This methodology compares experimental results with their numerical reproduction using the finite element method in order to obtain an estimation of the error between the results. This error estimation is then used by an evolutionary optimizer to determine, in an iterative process, the value of the material parameters which result in the best numerical fit. The novelty of the method is in the coupling between the simple genetic algorithm and the mixing theory used to numerically reproduce the composite behavior. The methodology proposed has been validated through a simple example which illustrates the exploitability of the method in relation to the modeling of damaged composite structures

On the feasibility of the computational modelling of the endoluminal vacuum-assisted closure of an oesophageal anastomotic leakage

Endoluminal vacuum-assisted closure (E-VAC) is a promising therapy to treat anastomotic leakages of the oesophagus and bowel which are associated with high morbidity and mortality rates. An open-pore polyurethane foam is introduced into the leakage cavity and connected to a device that applies a suction pressure to accelerate the closure of the defect. Computational analysis of this healing process can advance our understanding of the biomechanical mechanisms at play. To this aim, we use a dual-stage finite-element analysis in which (i) the structural problem addresses the cavity reduction caused by the suction and (ii) a new constitutive formulation models tissue healing via permanent deformations coupled to a stiffness increase. The numerical implementation in an in-house code is described and a qualitative example illustrates the basic characteristics of the model. The computational model successfully reproduces the generic closure of an anastomotic leakage cavity, supporting the hypothesis that suction pressure promotes healing by means of the aforementioned mechanisms. However, the current framework needs to be enriched with empirical data to help advance device designs and treatment guidelines. Nonetheless, this conceptual study confirms that computational analysis can reproduce E-VAC of anastomotic leakages and establishes the bases for better understanding the mechanobiology of anastomotic defect healing

Optimization method for the determination of material parameters in damaged composite structures

Abstract An optimization method to identify the material parameters of composite structures using an inverse method is proposed. This methodology compares experimental results with their numerical reproduction using the finite element method in order to obtain an estimation of the error between the results. This error estimation is then used by an evolutionary optimizer to determine, in an iterative process, the value of the material parameters which result in the best numerical fit. The novelty of the method is in the coupling between the simple genetic algorithm and the mixing theory used to numerically reproduce the composite behavior. The methodology proposed has been validated through a simple example which illustrates the exploitability of the method in relation to the modeling of damaged composite structures

On the feasibility of the computational modelling of the endoluminal vacuum-assisted closure of an oesophageal anastomotic leakage

Endoluminal vacuum-assisted closure (E-VAC) is a promising therapy to treat anastomotic leakages of the oesophagus and bowel which are associated with high morbidity and mortality rates. An open-pore polyurethane foam is introduced into the leakage cavity and connected to a device that applies a suction pressure to accelerate the closure of the defect. Computational analysis of this healing process can advance our understanding of the biomechanical mechanisms at play. To this aim, we use a dual-stage finite-element analysis in which (i) the structural problem addresses the cavity reduction caused by the suction and (ii) a new constitutive formulation models tissue healing via permanent deformations coupled to a stiffness increase. The numerical implementation in an in-house code is described and a qualitative example illustrates the basic characteristics of the model. The computational model successfully reproduces the generic closure of an anastomotic leakage cavity, supporting the hypothesis that suction pressure promotes healing by means of the aforementioned mechanisms. However, the current framework needs to be enriched with empirical data to help advance device designs and treatment guidelines. Nonetheless, this conceptual study confirms that computational analysis can reproduce E-VAC of anastomotic leakages and establishes the bases for better understanding the mechanobiology of anastomotic defect healing.Fil: Comellas, Ester. Centre Internacional de Mètodes Numèrics a l'Enginyeria; EspañaFil: Bellomo, Facundo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; ArgentinaFil: Rosales, Iván. B. Braun Surgical; EspañaFil: del Castillo, Luis F.. B. Braun Surgical; EspañaFil: Sánchez, Ricardo. B. Braun Surgical; EspañaFil: Turon, Pau. B. Braun Surgical; EspañaFil: Oller, Sergio Horacio Cristobal. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; Argentina. Centre Internacional de Mètodes Numèrics a l'Enginyeria; España. Universidad Politécnica de Catalunya; Españ